Improved parallel algorithms for the depth-first search and monotone circuit value problems

  • Authors:

  • Peter Varman;Kshitij Doshi

  • Affiliations:

  • Department of Electrical and Computer Engineering, Rice University, Houston, Texas;Department of Electrical and Computer Engineering, Rice University, Houston, Texas

  • Venue:
  • CSC '87 Proceedings of the 15th annual conference on Computer Science
  • Year:
  • 1987

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Abstract

Parallel algorithms for ordered depth-first search (ODFS) and the monotone circuit value (MCV) on parallel random access machines (PRAMs) and single bus multiprocessors are presented. While it is known that these problems are log-space complete for P and hence unlikely to have poly-logarithmic time parallel solutions, parallel algorithms that achieve a speedup linear in the number of processors (albeit within a limited range) are of considerable practical interest. In this paper we present parallel algorithms for these problems that require O(m/p + n) time on a p processor Concurrent Read Exclusive Write (CREW) PRAM, where n is the number of vertices and m the number of edges in the problem graph. This bound has previously been achieved only on more powerful PRAM models, namely the arbitrary Concurrent Read Concurrent Write (CRCW) PRAM for the MCV problem and the priority CRCW PRAM for the ODFS problem. Our technique permits us to implement these algorithms efficiently on single bus multiprocessor architectures in time O(n2/p) for 1 ≤ p ≤ n. An interesting consequence of our algorithms is that the problems of finding the connected components, the biconnected and bridge connected components of an undirected graph, and the strongly connected components of a directed graph can all be solved with the same processor and time complexities.